# Sphere spins faster at poles/axis?

1. May 9, 2012

### KidWonder

My science teacher says that a sphere will spin at a greater speed at it's poles. He says that the equator would spin the slowest.

He says it's basic physics that speed=distance/time.

Poles have a shorter distance to make a revolution contrary to the equator therefore it would have a greater speed.

The exact Axis point will not spin at all.

I tell him that as the circumference of a circle increases, a single point along it has to travel faster to complete a revolution in the same amount of time.

Am I right or wrong?

Thanks Guys.
God bless

2. May 9, 2012

### ZapperZ

Staff Emeritus
All points on the sphere will have a constant angular velocity (which is the number of rotations per unit time), but the circumference (or equator) will have the fastest linear speed, since linear speed v is measured as r*w, where r is the distance from the axis of rotation, and w is the angular velocity that I mentioned earlier.

http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html

So yes, you are correct.

Zz.

3. May 9, 2012

### Whovian

Did your science teacher really say that? Complain to someone who can fire them or move to a different class/school. :)

Yes. In fact, this is the definition of average velocity. And it does have less distance to go in the same amount of time. Therefore, its speed is lower, not higher. $\vec{v}\ \alpha\ \Delta\vec{p}$, so I don't see where your teacher is coming from.

Probably from a severe mixup of stuff. If a sphere has a certain Angular Momentum, and its radius suddenly decreases somehow, but Angular Momentum is conserved, its angular velocity will increase. So he might be thinking that points closer to the axis of rotation move more quickly?

4. May 9, 2012

### KidWonder

Thanks Guys, I knew I was correct.

And Whovian, my science teacher actually said that it was basic physics that Velocity =distance/time .

I'll have too explain the reasoning to him, it feels really good to prove my teacher wrong.

Thanks again.

5. May 9, 2012

### Dickfore

Is the sphere you're talking about rigid? Because, if it was a ball of gas, then, viscosity would cause points near the Equator to slow down, and points near the poles to have a bigger flow velocity, as compared to a rigid sphere. Thus, the angular speed of points near the equator would be lower than near the poles.

6. May 9, 2012

### Gordianus

I think the OP refers to a simple, rigid sphere. As for the teacher's knlowledge......

7. May 9, 2012

### cjameshuff

Viscosity in the absence of some disturbance would lead to a fluid sphere at equilibrium rotating as a whole exactly like a solid sphere. Cyclonic weather patterns and such occur because the atmosphere is being pushed around by things like solar heating, which still might confuse him. Or perhaps he was somehow getting confused by the speeds of orbiting objects?

In any case, the teacher's position is unsalvageable, his own reasoning leads to a conclusion opposite of what he claims.

8. May 9, 2012

### Dickfore

This is true.

Yes, or a nuclear reaction in the interior of the "ball"

The point is that he did not specify what the "sphere" was. When one uses terms like poles, and Equator, isn't it reminiscent of celestial bodies? Maybe the teacher was talking about the rotation of some celestial body, and the op pulled it out of context.

9. May 9, 2012

### Staff: Mentor

Sun rotates with different speed at the poles than at the equator, but the difference is in exactly opposite direction - it is fastest at the equator.

10. May 9, 2012

### Whovian

Yea, something of the sort was one of my theories. Or perhaps the professor completely misspoke.

11. May 9, 2012

### Dickfore

True, and i believe the same holds for Jupiter as well.

12. May 9, 2012

### Whovian

And likely the other Gas Giants. (What is the Sun but a giant Gas Giant that's massive enough to initiate nuclear fusion in its core?)

13. May 9, 2012

### Dickfore

14. May 9, 2012

### 256bits

Perhaps the teacher was talking about an object on a rotating sphere moving from the equator to the poles. I suspect the teacher has been misquoted.

15. May 9, 2012

### KidWonder

I understand that you believe a High School Physics teacher would not say this but he did. I know exactly what he said, and we had a brief 3 minute conversation about the subject after school. His reasoning was because of the smaller revolution distance at the pole, it would have a greater velocity. I disagreed.

My teacher graduated with a degree in Geology but somehow teaches Physics.

And I was talking about a Rigid sphere.

I've recently came across this scientific theory that the reason the Sun magnetic shift every decade or so, had something to do with it's poles and equator spinning different velocities.

Pretty cool, eh?

16. May 10, 2012

### willem2

Note that the graph goes only from -60 to +60 degrees of latitude, and that the according to the article the maximum wind speeds are at -60 and +60 and the
speeds decrease to 0 at the poles.

The wind speed must decrease to 0 at the poles, because you'd a very large acceleration to make the wind go round a small circle round the poles. This is the same reason there's an eye in a hurricane.

17. May 10, 2012

### Staff: Mentor

I have read explanations based on the hairy ball theorem. There must be zero somewhere.

18. May 10, 2012

### 256bits

I stand corrected.
You are correct and your teacher needs to update his science knowledge.

19. May 11, 2012

### ZapperZ

Staff Emeritus
Show him the Hyperphysics link I gave earlier.

If he makes a mistake on "basic physics", as he called it, what other mistakes has he been teaching?

Zz.

20. May 11, 2012

### haruspex

Ask him to imagine he was trying to run fast enough westwards to keep the sun in the same apparent position. Would he rather try this at the equator or a few metres from the North pole?